Chen, G. Y.; Yang, X. Q.; Yu, H. A nonlinear scalarization function and generalized quasi-vector equilibrium problems. (English) Zbl 1130.90413 J. Glob. Optim. 32, No. 4, 451-466 (2005). Summary: Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. In this paper we introduce a nonlinear scalarization function for a variable domination structure. Several important properties, such as subadditiveness and continuity, of this nonlinear scalarization function are established. This nonlinear scalarization function is applied to study the existence of solutions for generalized quasi-vector equilibrium problems. Cited in 88 Documents MSC: 90C47 Minimax problems in mathematical programming 46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics 90C29 Multi-objective and goal programming 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) Keywords:existence; generalized quasi-vector equilibrium; scalarization method PDF BibTeX XML Cite \textit{G. Y. Chen} et al., J. Glob. Optim. 32, No. 4, 451--466 (2005; Zbl 1130.90413) Full Text: DOI References: [10] Gerth(Tammer), Chr. and Weidner, P. (1990), Nonconvex secparation theorems and some applications in vector optimization, Journal of Optimization Theory and Applcaiotns, 67, 297–320. · Zbl 0692.90063 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.